Model of endogenous growth the AK model

1. Model of Endogenous Growth: The AK
Model
Presented By
Guru Dayal Kumar
MA Economics
Central University of South Bihar
Email-gurudayal1996@gmail.com
Mob No-9128202376

2.  The AK model of economic growth is an endogenous
growth model used in the theory of economic growth, a
subfield of modern macroeconomics.
 In the 1980s it became progressively clearer that the
standard neoclassical exogenous growth models were
theoretically unsatisfactory as tools to explore long run
growth, as these models predicted economies
without technological change and thus they would
eventually converge to a steady state, with zero per capita
growth.
Introduction

3.  A fundamental reason for this is the diminishing return of
capital; the key property of AK endogenous-growth model
is the absence of diminishing returns to capital.
 In lieu of the diminishing returns of capital implied by the
usual parameterizations of a Cobb–Douglas production
function, the AK model uses a linear model where output is
a linear function of capital.
 Its appearance in most textbooks is to
introduce endogenous growth theory.
Conti…

4.  Y = AK
 where A is a positive constant that reflects the level
of technology and ‘K’ here is taken in a broader sense
as it includes physical as well as human capital.
 This model shows constant marginal product to
capital (as MPk = dY/dK=A) indicating that long run
growth is possible. Thus, AK model is a simple way of
illustrating endogenous growth.
Graphical Presentation

5. 
 Closed economy,
 The savings are equal to investment
 Under conditions of full employment.
Assuming

6.  Since savings are the function f income and capital
depreciates at a constant rate i.e. ‘δ’ the
 change in capital stock can be traced through following
equations.
 I = S = s.Y = s.AK
 and, since capital depreciates at a constant rate, the change
in capital stock i.e. can be expressed as = 𝑠. 𝑌 − 𝛿. . This
change in capital stock can also be represented by a
diagram given below.

7. Figure

8.  In this figure Y-axis show output per worker while the X-axis
show the capital stock.
 The line Y=AK having a constant slope shows the constant
marginal productivity of capital; the line S=s.Y is the gross
investment line while the line δK shows the depreciation line
or the total replacement investment.
 The difference between the gross investment line and the
replacement line i.e. area between S=s.Y line and δK line
shows net investment in the economy which is positive
and increasing.

9.  The growth of capital stock can be found by dividing both sides of the
equation showing change in capital stock with ‘K’, we get
𝐾°
𝐾
=s.
𝑌
𝐾
-𝛿
 Since, Y=AK, i.e. Y/K =A, therefore, above equation can be rewritten as
𝐾°
𝐾
=s.A-𝛿
 As, growth of output is equal to the growth of capital stock,
𝑌°
𝑌
=
𝐾°
𝐾
=s.A-𝛿


10.  An improvement in the level of technology,
 A, which raises the marginal and average products of
capital, also raises the growth rate and alters the saving
rate.
 We have to focus on changes in various kinds of
government policies amount to shifts in A;
 that is, we can generalize the interpretation of the
parameter A to go beyond literal differences in the level of
the production function.

11.  In contrast to the effects on long-run growth in the AK
model,
 Ramsey model implies that the long-run per capita growth
rate is pegged at the value x, the exogenous rate of
technological change.
 A greater willingness to save or an improvement
in the level of technology shows up in the long run as higher
levels of capital and output per effective worker but in no
change in the per capita growth rate.

12.  Thank You